Question

Is the following shape a rectangle? How do you know?

Answer 1

Answer: The answer is (D). No, the adjacent sides are not perpendicular.

Step-by-step explanation: We are given a shape on the co-ordinate plane and we are to check the correct statement about the shape from the given options.

The shape has four vertices A(4, -1), B(2, 4), C(-2, 2) and D(0, -3). So, the shape is definitely a quadrilateral. We are to check whether it is a rectangle or not.

We will find the slope of all the sides AB(m), BC(n), CD(o) and DA(p) as follows:

`m=(4+1)/(2-4)=-(5)/(2),\\\\n=(2-4)/(-2-2)=(1)/(2),\\\\o=(-3-2)/(0+2)=-(5)/(2),\\\\p=(-3+1)/(0-4)=(1)/(2).`

Since,

`m=o,~~n=p,`

so the opposite sides are parallel, but

`m* n\\eq -1,~~n* o\\eq -1,~~o* p\\eq -1,~~p* m\\eq -1,`

so the adjacent sides are not perpendicular.

Thus, (D) is the correct option.